Question

A 10-year study conducted by the American Heart Association provided data on how age, blood pressure, and smoking relate to the risk of strokes. Data from a portion of this study follow. Risk is interpreted as the probability (times 100) that a person will have a stroke over the next 10-year period. For the smoker variable, 1 indicates a smoker and 0 indicates a nonsmoker.

Risk		Age	Blood Pressure		Smoker
14		58	201		0
23		82	98		1
25		74	171		0
68		85	142		0
31		82	188		0
51		62	198		0
18		81	189		0
24		78	147		1
43		78	216		0
32		77	206		1
40		81	141		0
30		74	124		0
20		65	132		0
57		61	187		0
41		60	168		0
36		80	187		0
36		83	144		0
34		59	166		0
8		55	105		1
42		68	216		0

a. Develop an estimated regression equation that can be used to predict the risk of stroke given the age and blood pressure level. Enter negative value as negative number.

The regression equation is (to 4 decimals)

Risk=___________+_________age+________ blood pressure

s=__________ (to 4 decimals) R2=_________ (to 4 decimals) R2 adj=_______ (to 4 decimals)

Analysis of Variance

SOURCE DF SS (to 2 decimals) MS (to 2 decimals) F (to 2 decimals) p-value (to 4 decimals) Regression Residual --------------- ------------- Total ---------------- --------------- ----------------

b. Consider adding two independent variables to the model developed in part (a), one for the interaction between age and blood pressure level and the other for whether the person is a smoker. Develop an estimated regression equation using these four independent variables. Enter negative value as negative number. Use Table 4 in Appendix B.

The regression equation is (to 4 decimals)

Risk=_________+_________age+_________blood pressure+____________smoker+_____________ageblood press

s=__________ (to 4 decimals) r2=__________ (to 4 decimals) r2 adj=________ (to 4 decimals)

Analysis of Variance

SOURCE DF SS (to 2 decimals) MS (to 2 decimals) F (to 2 decimals) p-value (to 4 decimals) Regression Residual ------------- ------------- Total ------------------ -------------- ---------------

c. At a= .05 level of significance, test to see whether the addition of the interaction term and the smoker variable contribute significantly to the estimated regression equation developed in part (a). Use Table 4 in Appendix B.

What is the value of the F test statistic?
___________________ (to 2 decimals)

p-value is - (Select your answer -lower than 0.01,between 0.01 and 0.025,between 0.025 and 0.05,between 0.05 and 0.10,greater than 0.10), so the addition of the two independent variables - (Select your answer -is, is not) statistically significant.

Answer 1

a)

using excel data analusis tool for regression,

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.349047
R Square	0.121834
Adjusted R Square	0.01852
Standard Error	14.49719
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	2	495.6859	247.843	1.179259	0.331439
Residual	17	3572.864	210.1685
Total	19	4068.55
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-8.13902	29.8608	-0.27257	0.78847	-71.1398	54.86176	-71.1398	54.86176
Age	0.292732	0.333263	0.878382	0.391983	-0.41039	0.995857	-0.41039	0.995857
Blood Pressure	0.124284	0.093721	1.326107	0.202347	-0.07345	0.322017	-0.07345	0.322017

Risk = -8.1390 + 0.2927 age+ 0.1243 blood pressure

s = 14.4972

R Square   0.1218
Adjusted R Square   0.0185

ANOVA
	df	SS	MS	F	p-value
Regression	2	495.69	247.84	1.18	0.3314
Residual	17	3572.86	210.17
Total	19	4068.55

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SUMMARY OUTPUT
Regression Statistics
Multiple R	0.555321
R Square	0.308382
Adjusted R Square	0.12395
Standard Error	13.69643
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	4	1254.667	313.6668	1.672067	0.208546
Residual	15	2813.883	187.5922
Total	19	4068.55
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-129.811	108.6646	-1.1946	0.250792	-361.424	101.8026	-361.424	101.8026
Age	2.132009	1.470587	1.449767	0.167709	-1.00247	5.26649	-1.00247	5.26649
Blood Pressure	0.902803	0.663086	1.361517	0.193452	-0.51053	2.316137	-0.51053	2.316137
Smoker	-10.6991	8.513545	-1.25671	0.228076	-28.8453	7.44712	-28.8453	7.44712
age*blood pres	-0.01156	0.009058	-1.27594	0.221383	-0.03086	0.007749	-0.03086	0.007749

Risk = -129.811 + 2.1320 age + 0.9028 blood pressure -10.6991 smoker -0.0116 ageblood press

s=13.6964

R Square   0.3084
Adjusted R Square   0.1240

ANOVA
	df	SS	MS	F	p-value
Regression	4	1254.67	313.67	1.67	0.2085
Residual	15	2813.88	187.59
Total	19	4068.55

c)

value of the F test statistic = 1.67

p-value = greater than 0.10

so the addition of the two independent variables is not statistically significant